A Novel Euler’s Elastica-Based Segmentation Approach for Noisy Images Using the Progressive Hedging Algorithm

Euler’s elastica-based unsupervised segmentation models have strong capability of completing the missing boundaries for existing objects in a clean image, but they are not working well for noisy images. This paper aims to establish a Euler’s elastica-based approach that can properly deal with the random noises to improve the segmentation performance for noisy images. The corresponding formulation of stochastic optimization is solved via the progressive hedging algorithm (PHA), and the description of each individual scenario is obtained by the alternating direction method of multipliers. Technically, all the sub-problems derived from the framework of PHA can be solved by using the curvature-weighted approach and the convex relaxation method. Then, an alternating optimization strategy is applied by using some powerful accelerating techniques including the fast Fourier transform and generalized soft threshold formulas. Extensive experiments have been conducted on both synthetic and real images, which displayed significant gains of the proposed segmentation models and demonstrated the advantages of the developed algorithms.